Not necessarily. There are several factors involved when selecting a filler metal. They include (but not limited to):

Whether it is necessary to match the chemistry of the base metal, such as in the case where it is necessary to consider corrosion resistance.

Whether the joint is highly restrained where enhanced ductility is desirable . Patches in vessels and piping systems should always be considered to be highly restrained. Thick joints are typically considered to be highly restrained. In both cases or in any case considered to highly restrained it is often advantageous to select a filler metal with lower strength, but high ductility provided it is compatible with the base metals being jointed.  There are numerous advantages to match the strength of the lower strength base metal. The connection can be no stronger than the weaker base metal, i.e., "the weak link." the strength of the joint will actually increase by a the mechanism of strain hardening. In the case of carbon and low alloy steels the increase in strength can be on the order of 10 ksi. 

A transitional filler metal may be required where the two base metals have different coefficients of expansion or where the two base metals have dissimilar properties or may be incompatible. Consider a carbon steel joined to a copper based alloy, in which case the copper based alloy may be surfaced with a nickel filler metal, likewise the carbon steel surfaced with nickel and then the two welded together.

Carbon steels are often surfaced with type 309 stainless before being surfaced with type 316 to provide the proper microstructure.

In the case of aluminum alloys, some such as 6061-T6 need to be welded with a filler metal and diluted to produce a weld that will not easily crack. It cannot be welded with a matching filler metal. Likewise, type 304 stainless is not welded with 304 filler metal because a filler metal with sufficient, but not too much ferrite, is produced. Have you ever seen type 304 stainless filler metal?

As you can see, there are other considerations beyond strength.

Best regards - Al